How can we argue that it was right and proper for the U.S to make claims such as the Monroe Doctrine?
The best way to make this argument is by saying that powerful countries having spheres of influence is an aspect of international relations that will probably never go away. Such spheres of influence were even more common at the time that the US issued the Monroe Doctrine. When a practice is common in international relations, it is hard to argue that it is not right or proper for any given country to engage in that practice.
You can further argue that the Monroe Doctrine at least had a partially laudable goal. It was meant in part to protect the countries of the New World from being colonized by European countries. The US may not have been trying to be philanthropic, but that is a worthy cause.